. Consumption Suppose that a household lives for two periods and has a utility function and intertemporal budget constraint as follows: a) Derive step by step the Euler equation faced by this consumer (dene the Lagrangian and then obtain rst order conditions as we did it in the lecture). Explain the intuition of the Euler equation. b) Find a solution for optimal consumption in both period 1 and 2 as a function of the parameter 6 as well as the variables 1', yl and y2. c) What is the ceteris paribus effect on consumption today (c1) and tomorrow (6;) of the following shocks: (i) An increase in 3. (ii) A decrease in lifetime income. (iii) An increase in y. d) Is there a condition where cl= (2;? If so, what value must [3 assume